Interpretation of dx/dt and u in CFD

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I americium presently studying CFD and I person a mobility astir really I should construe nan word u and dx/dt. I would for illustration to find that retired successful nan textbook, but I could not.

When I lick 1D Euler Equation pinch Mass conservation

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, past I get nan result

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In nan consequence I person a problem astir really to construe these 2 position u and dx/dt. As I understand, some position were nan travel velocity for illustration u=dx/dt. The truth that nan meaning of these position diverges confuses me.

Thanks for your reply successful beforehand and person a bully weekend.